\sect{Fermions in a gravitational field}
%Baruch's B12.
Consider fermions of mass $\mass$ and spin $1/2$ in a gravitational field
with constant acceleration $g$ and at uniform temperature $T$.
The density of the Fermions at zero height is $n(0)=n_{0}$.
In item (3) assume that at zero height the fermions form a degenerate
gas with Fermi energy $\epsilon_{F}^{0}$ that is much larger compared with~$T$.
\begin{enumerate}
\item Assume that the fermions behave as classical particles and
find their density $n(h)$ as function of the height.
\item Assume $T=0$. Find the local Fermi momentum $p_{F}(h)$
and the density $n(h)$ as function of the height.
\item Assume low temperatures. Estimate the height $h_{c}$ such that
for $h\gg h_{c}$ the fermions are non-degenerate.
\item In the latter case find $n(h)$ for $h\gg h_{c}$, given as before $n_0$ at zero height.
\end{enumerate}
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